Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin

Foreword

Report of TAC 62 held in Washington, October 18-23, 1993, Alex McCalla presiding. TAC discussed the report of the CGIAR Steering Committee on International Livestock Research. It agreed that the expertise of existing IARCs should not dominate the new center. TAC commissioned a stripe study of plant genetic resources to recommend options to TAC for a change in CGIAR strategy which would recognize its place in a global system of biodiversity. The Committee agreed that the document on CGIAR resource allocation for 1994-1998 submitted to ICW accurately reflected its views. It also endorsed the version of Chapter 13 of the Report on CGIAR Priorities and Strategies as submitted to ICW.Issues on various aspects of the process for external reviews of centers raised in the ICARDA EPMR were discussed by TAC alone, and in a joint session with center directors and board chairs. TAC agreed to experiment with new ideas of strengthen the process. TAC decided to undertake a strategic stripe study of public policy and public management research, but asked for greater definition of the boundaries of the study. It also endorsed a proposal, discussed at TAC 61, to study CGIAR delivery mechanisms, starting in West Africa. TAC further agreed on an inter-center study of CGIAR research on roots and tubers in conjunction with the external reviews of CIP, CIAT and IITA.TAC held a critical discussion of the activities proposed to follow up on UNCED by the CGIAR task force headed by Stein Bie, and made a number of comments for consideration of the Group. The Committee reviewed and revised the criteria for the King Baudouin Award

On the Minimal Uncompletable Word Problem

Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested in finding bounds on the minimal length of words in Sigma* which are not elements of Fact(S*) in terms of the maximal length of words in S.Comment: 5 pages; added references, corrected typo

On subtrees of the representation tree in rational base numeration systems

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Finite-State Methods and Models in Natural Language Processing

The article presents a short overview to the state of the art and relates the articles in this issue into currently active/open research problems. WOS:000289532400001Peer reviewe

Contributions à l'étude de la dérivation des expressions rationnelles et à l'étude des systèmes de numération abstraits

Les travaux de cette thèse s'inscrivent dans la théorie des automates et des langages formels. ils peuvent se diviser en deux parties qui donnent également deux visions différentes de manipuler les langages dans la théorie des automates. La première partie s'intéresse à la notion de dérivation des expressions qui permet de faire passer le formalisme des quotients de langages au niveau des expressions rationnelles. en particulier cette thèse étudie les termes dérivés cassés d'une expression rationnelle. ces termes dérivés cassés permettent, sous certaines circonstances, et à l'aide d'autres opérations, une réversibilité de la transformation d'un automate en une expression rationnelle. Dans la seconde partie, la théorie des automates est utilisée pour traiter des problèmes sur les systèmes de numération. les systèmes de numération représentent des nombres par des mots. il est possible d'utiliser des automates et des transducteurs afin d'être capable de 'compter' sur un langage rationnel représentant les entiers. plus précisément ces automates sont étudiés pour le cas des systèmes de numération abstraits qui associent à chaque entier un mot d'un langage rationnel, ordonné par l'ordre radiciel. dans un tel système, la fonction qui permet de calculer le mot suivant est une fonction co-séquentielle par morceaux, c'est-à-dire qu'il suffit de lire deux fois le mot d'entrée de la droite vers la gauche pour qu'une machine calcule son image.The works in this thesis lies in the automata and formal languages theory. in the first part, the notion of derivation of rational expressions is studied. more precisely the broken derived terms of a rational expressions. Theses broken derived terms allow, under certain circumstances, with some other operations on automata, to have the reversibility of the transformation of an automaton into a rational expression. In the second part, automata and tranducers allow to 'count' on a numeration system, where integers are represented by words on a rational language. more precisely, this part adress the problem of counting in an abstract numeration systems, which maps to any word of a rational language, ordored by radix order, the integer corresponding to the order of the word. in such a numeration system, the function which computes the successor of a word is a piecewise co-sequential function: it can be realised by a machine which reads the input two times to give the output.PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF